Fighting raged across Syria on Friday as Bashar al-Assad's armed forces pounded opposition strongholds after the shock resignation of the UN peace envoy Kofi Annan left the international community scrambling for effective policies.

Rebel-held areas of the northern city of Aleppo came under attack from artillery, helicopters and fighter jets, though an expected government ground offensive did not materialise. The UN had predicted on Thursday that an attack was imminent. Battles erupted near the heart of Aleppo for the first time in the fortnight-long battle. Rebels claimed to control parts of the northeast, east and south of the city, but western Aleppo remained a regime stronghold.

The battle for Syria's second city appears to be nearing a decisive phase with reinforcements continuing to bolster the Free Syrian Army (FSA) ranks. Several hundred fighters arrived from Idlib and Hama and rebel leaders say thousands more are expected before what they claim will be new phase in the fight sometime next week.

The road northeast from Aleppo through al-Bab to the Turkish border is now in regime hands, securing a vital supply line to Turkey.

Regime jets continued to soar across the skies of Aleppo as did helicopters. Rebel leaders believe that regime forces would fight till the end to defend the centre of the world's oldest city and are congregating around key government buildings and renowned landmarks such as the Grand Mosque and the ancient citadel in the centre.

Video clips posted on the internet showed columns of smoke rising from the Salahedin neighbourhood after an attack by unidentified combat planes. Another image showed a girls' school badly damaged, apparently by shell fire, though it remains impossible to verify the content of the videos.

"Fighting seems to have really intensified," reported a local activist who tweets as Edward Dark. "But no side seems to have the upper hand for now." On Thursday hundreds of elite Republican Guards were seen arriving at the city's airport. Food and fuel shortages and the humanitarian situation have worsened.

In Damascus at least 20 people were reported killed late on Thursday when mortar shells hit the Yarmouk Palestinian refugee camp in an apparent spillover from fighting in the nearby suburb of Tadamon, where the government used tanks and armoured vehicles to drive out fighters of the FSA. A lack of fuel prevented the transportation of the injured to field hospitals. Sana, the Syrian state news agency, blamed the bombardment on "terrorist mercenaries".

Violence was also reported from Homs and Hama in the centre of Syria, Deir al-Zour in the east and Dera'a in the south, attesting to the fact that the uprising has spread throughout the country.

Annan's resignation statement that the increasing militarisation of the conflict was making his mission impossible has been borne out by reports of government forces using artillery and air power and the rebels using tanks for the first time to attack a military airport north of Aleppo.

Control of Aleppo is crucial not only because of its size but also because it could help the opposition carve out a safe zone across the whole of northern Syria including the Turkish border.

The former UN chief blamed the international community for "finger-pointing" and recriminations which had undermined his mission to mediate in the 17-month long uprising, which has claimed an estimated 20,000 lives.

But Annan's six-point peace plan, based on a ceasefire that never took hold and UN monitors who could report on killings but not stop them, had been moribund for weeks before he quit.

William Hague, the foreign secretary, admitted on Friday that diplomacy had failed but he insisted that efforts to deal with Syria would continue. "Diplomacy has not worked so far, diplomacy has so far failed the people of Syria," Hague told the BBC. "That doesn't mean that we give up on diplomacy."

Alistair Burt, the junior Foreign Office minister responsible for the Middle East, confirmed the UK would be providing further communications equipment to the opposition in Syria in the next month. It has already provided humanitarian assistance and other "non-lethal" aid.

US media reported this week that President Barack Obama has signed a covert order authorising support, presumably by the CIA, for Syrian rebels, but that is not thought to include weapons deliveries.

In New York, the UN general assembly which comprises all 193 member states, was preparing to vote on a resolution condemning Syria's use of heavy weapons and protesting at the failures of the security council, where the five permanent member states have vetoes. The text was put forward by Saudi Arabia, which openly supports the anti-Assad rebels. The Syrian UN ambassador, Bashar Ja'afari, called it a "strange paradox" that the states which were sponsoring the resolution were fuelling the violence.

The language was watered down by removing a demand that Assad resign and a call for other countries to impose sanctions on Syria. It still criticised Russia and China – which have three times vetoed action against Syria – by "deploring the security council failure" to act.

Ban ki-Moon, the UN secretary-general, told the assembly before the vote: "As we meet here, Aleppo … is the epicentre of a vicious battle between the Syrian government and those who wish to replace it. The acts of brutality that are being reported may constitute crimes against humanity or war crimes. Such acts must be investigated and the perpetrators held to account."

Amnesty International urged the Free Syrian Army to carry out an "impartial, independent and comprehensive" investigation into the killings of 14 members of the Berri clan in Aleppo this week. Members of the Sunni pro-government clan were shown in a video, allegedly filmed by the FSA, being shot dead. The FSA described what appeared to be a summary execution as revenge for killings of its fighters, but later condemned it.

"Killing captives is a serious violation of international humanitarian law and a war crime," warned Amnesty's Middle East and North Africa director Philip Luther. "The FSA leadership have a duty to end such violations immediately."

The Russian defence ministry denied reports that Moscow is sending three warships carrying some 360 marines to the Syrian port of Tartous.